Question: Multiply the following complex numbers, marked as blue dots on the graph: $(3 e^{\pi i / 3}) \cdot ( e^{5\pi i / 6})$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $3 e^{\pi i / 3}$ ) has angle $\frac{1}{3}\pi$ and radius $3$ The second number ( $ e^{5\pi i / 6}$ ) has angle $\frac{5}{6}\pi$ and radius $1$ The radius of the result will be $3 \cdot 1$ , which is $3$ The angle of the result is $\frac{1}{3}\pi + \frac{5}{6}\pi = \frac{7}{6}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{7}{6}\pi$.